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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Free products of von Neumann algebras


Author: Wai Mee Ching
Journal: Trans. Amer. Math. Soc. 178 (1973), 147-163
MSC: Primary 46L10
DOI: https://doi.org/10.1090/S0002-9947-1973-0326405-3
MathSciNet review: 0326405
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Abstract: A new method of constructing factors of type ${\text {II}_1}$, called free product, is introduced. It is a generalization of the group construction of factors of type ${\text {II}_1}$ when the given group is a free product of two groups. If ${A_1}$ and ${A_2}$ are two von Neumann algebras with separating cyclic trace vectors and ortho-unitary bases, then the free product ${A_1} \ast {A_2}$ of ${A_1}$ and ${A_2}$ is a factor of type ${\text {II}_1}$ without property $\Gamma$.


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Keywords: von Neumann algebra, group construction factor of type <!– MATH ${\text {II}_1}$ –> <IMG WIDTH="30" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${\text {II}_1}$">, free product, property <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img10.gif" ALT="$\Gamma$">
Article copyright: © Copyright 1973 American Mathematical Society